DNA damage activates a signalling network that blocks cell-cycle progression, recruits DNA repair factors and/or triggers senescence or programmed cell death. Alterations in chromatin structure are implicated in the initiation and propagation of the DNA damage response. Here we further investigate the role of chromatin structure in the DNA damage response by monitoring ionizing-radiation-induced signalling and response events with a high-content multiplex RNA-mediated interference screen of chromatin-modifying and -interacting genes. We discover that an isoform of Brd4, a bromodomain and extra-terminal (BET) family member, functions as an endogenous inhibitor of DNA damage response signalling by recruiting the condensin II chromatin remodelling complex to acetylated histones through bromodomain interactions. Loss of this isoform results in relaxed chromatin structure, rapid cell-cycle checkpoint recovery and enhanced survival after irradiation, whereas functional gain of this isoform compacted chromatin, attenuated DNA damage response signalling and enhanced radiation-induced lethality. These data implicate Brd4, previously known for its role in transcriptional control, as an insulator of chromatin that can modulate the signalling response to DNA damage.